In much of the English-speaking world, including in the U.K. and especially in Australia, wellbeing is usually one word, with no hyphen. Though the hyphenated form is older and remains acceptable everywhere, the one-word form has existed for several centuries and has grown steadily more common over the years. Today it is not questioned outside North America.
In the U.S. and Canada, meanwhile, the one-word form remains rare, appearing only a small fraction of the time. In North America, the word is hyphenated, well-being. Spell check doesn’t catch wellbeing, and that form does appear occasionally in edited texts, but its rarity suggests it still has a long way to go before gaining full acceptance.